Consistently +6? That is a VERY precise watch! Precision speaks more to the quality of a movement than does the accuracy, which can be easily adjusted if the watch is precise. Having someone open the watch can introduce more problems.

"The fact that the mechanism is quite unnecessary merely adds to its charm." - George Daniels

I find that method works for adjusting such small increments of time as +/- 6. There's a chart on Google that shows the positions for speeding up and slowing down the time by small increments. My Sub Hulk is within a few seconds a month.

My Master Compressor Geographic was constantly gaining time when I kept it crowns down overnight. When I tried different positions overnight for the watch, I found crowns up kept it accurate under a minute per month.

Agreed and the point is the consistency of +6 which is well below the 10 seconds mark.
Consistency is showing the watch is running well. Some watches run slightly slower or faster due to changes in temperature, too.
Consistency of +/- 0 second or +/- 2 seconds somehow spoils the fun of owning a mechanical watch. My point is please do not let this +6 seconds put pressure on the pleasure of ownership. :)

Depending on many factors - power reserve, watch position at rest, etc. - you might be chasing the impossible dream. What if you get it back and it's spot on, but after a month of living with it in your normal daily routine it goes off by 6-10 seconds? Or you don't wear it for a period of time and it's in the face up, or vertical position and it speeds up or slows down on the winder?

There are many factors that affect how a mechanical watch keeps time. Hopefully these factors don't end up having you jousting with windmills ;0).

The most expensive 6 seconds I ever got back in my life, but for a watch that otherwise keeps time very consistently, I'm going to enjoy wearing it a lot more. Keeps up with my other 2 automatics (Omegas) which are within + 1-2 sec/week. Modern automatics are pretty amazing to be able to keep time like that.

I used to let myself be bothered by the same thing but anymore, unless it's way of, I don't even give it thought. I haven't even checked the accuracy of my last two purchases. Sure beats being all bent out of shape checking it against my atomic click every 12 hours! Don't let it bother you, it's a mechanical device, and a very sensitive one.